Generation of multi-resolution image pyramids

ABSTRACT

Embodiments are described for a system and method for generating a multi-resolution image pyramid. The method can include obtaining an image captured as a coarse image of a defined subject and a fine image of the defined subject. The fine image can be downsampled to create a temporary image. A further operation is applying a structure transfer operation to the temporary image to transfer color detail from the coarse image. The structure transfer takes place while retaining structural detail from the temporary image. A blending operation can be applied between the temporary image and the fine image to construct an intermediate image for at least one intermediate level in the multi-resolution image pyramid between the fine image and the coarse image.

BACKGROUND

In the computer graphics and GIS (Geographic Information System)communities, the topic of stitching and fusing collections of images toform seamless maps or panoramas has been studied extensively. Suchimaging techniques have been used to assemble the large datasetsavailable on Internet services like Keyhole, TerraServer, Bing™ Maps,Google™ Maps, and Yahoo® Maps.

Multiresolution datasets often incorporate several sources of imagery atdifferent scales. For instance, satellite images can be provided at acoarse resolution and aerial photographic images can be used at finerresolutions. Zooming within these maps may reveal jarring transitions.The data sources from which images are drawn often vary significantly inappearance due to differences in spectral response, seasonal changes,lighting and shadows, and custom image processing. Specifically, zoomingin or out within a multiresolution image pyramid often results in abruptchanges in appearance (i.e. temporal “popping”). In addition, spatialdiscontinuities may be observed in static perspective views, as suchviews access several image pyramid levels simultaneously.

SUMMARY

This summary is provided to introduce a selection of concepts in asimplified form that are further described below in the detaileddescription. This summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used to limit the scope of the claimed subject matter. While certaindisadvantages of prior technologies are noted above, the claimed subjectmatter is not to be limited to implementations that solve any or all ofthe noted disadvantages of the prior technologies.

Various embodiments are described for a system and method for generatinga multi-resolution image pyramid. The method can include obtaining animage captured as a coarse image of a defined subject and a fine imageof the defined subject. The fine image can be downsampled to create atemporary image. A further operation is applying a structure transferoperation to the temporary image to transfer color detail from thecoarse image. The structure transfer takes place while retainingstructural detail from the temporary image. A blending operation can beapplied between the temporary image and the fine image to construct anintermediate image for at least one intermediate level in themulti-resolution image pyramid between the fine image and the coarseimage.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an embodiment of multi-resolution image pyramid withmultiple resolutions of an upsampled image.

FIG. 2 is a flowchart illustrating an overview of a method forgenerating a multi-resolution image pyramid in an embodiment.

FIG. 3 is a block diagram illustrating an embodiment of a method forcreating a multi-resolution image pyramid.

FIG. 4 is an illustration of an embodiment of the z-score and rankproperties that may be used for windowing transfer calculations.

FIG. 5 is flowchart illustrating an embodiment of a method forgenerating an image that includes image structure detail from a fineimage and color from a coarse image.

FIG. 6 is a chart illustrating an embodiment of a process used inclipped Laplacian blending.

FIG. 7 illustrates an embodiment of a process for an efficient blendingmethod for clipped Laplacian blending.

FIG. 8 is a flow chart illustrating an embodiment of efficientoperations for generating a multi-resolution image pyramid used invisual transitions across multiple viewing scales.

FIG. 9 is a block diagram illustrating an embodiment of modules that maybe used for generating a multi-resolution image pyramid used in visualtransitions across multiple viewing scales.

DETAILED DESCRIPTION

Reference will now be made to the exemplary embodiments illustrated inthe drawings, and specific language will be used herein to describe thesame. It will nevertheless be understood that no limitation of the scopeof the technology is thereby intended. Alterations and furthermodifications of the features illustrated herein, and additionalapplications of the embodiments as illustrated herein, which would occurto one skilled in the relevant art and having possession of thisdisclosure, are to be considered within the scope of the description.

A visually smooth image pyramid can be created that combines differentdata sources at different scales. Such image pyramids are used totransition between lower resolution images and higher resolution imagesin computer generated image environments. Examples of such computergenerated image environments may include: simulations, games, maps,medical images, and other environments where a smooth transition isdesired between a coarse resolution image and a fine resolution image.

The input imagery for the image pyramid exists at a subset of levels andthe imagery may already be spatially stitched together using existingstitching techniques. While the problem of creating an image pyramid mayseem simple, several straightforward approaches have drawbacks. Onesimplistic idea is to downsample the fine imagery all the way to thecoarsest level of the pyramid, overwriting any coarser image content.Downsampling or sub-sampling is the process of reducing the samplingfrequency for an image created from an original graphic image. However,fine-scale imagery is often sparsely defined, and the resulting coarserlevels may have a non-uniform appearance. Instead, it is desirable topreserve the spatial consistency of the coarse-scale image.

Another possible approach is to modify the fine-scale imagery to havethe same color appearance as the coarse-scale content. However, thecolor histogram of the fine image is often richer and the colorhistogram of the fine image may be preferred. In particular, thedifferences in appearance at the edges of images and across levels of animage pyramid can be noticeable in static perspective views. Similarly,the solution of replacing coarse pyramid levels by downsampling thesparse fine imagery may lead to a patchwork appearance at coarserlevels.

In order to address these issues, the present technology can create animage pyramid 100 with multiple resolutions of an upsampled image, asillustrated in FIG. 1, from stitched imagery at several scales thatprovides smoother visual transitions when zooming occurs. The presenttechnology provides techniques that improve the transitions betweenimages. One technique called structure transfer is a nonlinear operatorthat combines the detail of one image with the local appearance ofanother image. This operation can be used to inject detail from a fineimage 130 into a coarse image 110 while retaining color consistency. Theimproved structural similarity provided in intermediate resolutionimages 120 from the structure transfer operation significantly reducesinter-level ghosting artifacts. The second technique can be calledclipped Laplacian blending and this blending technology can be anefficient construction to minimize blur when creating intermediatelevels. Such blending considers the sum of all inter-level imagedifferences within the pyramid.

This process can simultaneously satisfy both multi-resolution andspatial continuity. As a result, the visual differences between adjacentlevels of the image pyramid can be minimized. In addition, the colorcharacteristics of both the coarse and fine imagery can be preserved.

The visual difference between two images is often measured using themean squared error (MSE) of corresponding pixels. While this simplepoint wise metric leads to convenient linear systems, it does notaccurately capture the perceptual characteristics of the human visualsystem. Rather, a metric that emphasizes structural similarity (SSIM)can be more effective. In particular, minimizing MSE alone results in animage pyramid with severe ghosting artifacts. One problem with simplyminimizing MSE is that the coarse and fine images have differences instructural detail due to misregistration, parallax, or many otherunavoidable factors in image acquisition and processing. Explicitlyconsidering structural similarity helps to overcome ghosting.

Maximizing structural similarity is generally a nonlinear problem andtherefore expensive to solve directly. To attain an efficient solution,the problem can be divided into two parts. First, a structure transferoperation can be used to maximize structural compatibility. Thisoperation can modify the coarse image to inherit the detail of the fineimage while preserving its original local color characteristics.

Second, once the structurally compatible images have been created, thesum of all inter-level image differences within the pyramid can beminimized using the MSE metric. This difference function can be definedjudiciously to avoid signal blurring. Although minimizing MSE is alinear problem, a global solution over all pixels in a large imagepyramid is still costly. A good approximate solution can be found usingan efficient construction with clipped Laplacian blending.

FIG. 2 is a flowchart illustrating a high level overview of anembodiment of a method for generating a multi-resolution image pyramid.The method can include the operation of obtaining an image captured as acoarse image of a defined subject, as in block 210. An example of acoarse image is a satellite image of certain geographic area (e.g., aLandsat image) or a coarse texture that is applied to a 3-D geometricobject. An image can also be captured as a fine image of the definedsubject, as in block 220. An example of a coarse image is an aerialphotographic image of the same geographic area as the coarse image or afine texture that is applied to a 3-D geometric object. The coarse imageand fine image of the defined subject can be obtained from a computerreadable storage medium or a computer memory.

The fine image can then be downsampled to create a temporary image, asin block 230. A structure transfer operation can then be applied to thetemporary image to transfer color detail from the coarse image, whileretaining structural detail from the temporary image, as in block 240.

A blending operation can be applied between the temporary image and thefine image to construct an intermediate image for at least oneintermediate level in the multi-resolution image pyramid between thefine image and the coarse image, as in block 250. The operations ofapplying a structure transfer operation and applying a blendingoperation to the temporary image can be performed on a server by acomputer processor.

In one embodiment, the blending operation can be clipped Laplacianblending. The Laplacian blending may include applying a blendingoperation that blends a Laplacian pyramid from the fine image with aLaplacian image generated from the coarse image. A fine Laplacian imagepyramid can be formed that has a plurality of downsampled images fromthe fine image. Similarly, a coarse Laplacian image pyramid can beconstructed from a plurality of downsampled images from the coarseimage. A Laplacian pyramid represents a single image as a sum of detailat different resolution levels. In other words, a Laplacian pyramid is abandpass image pyramid obtained by forming images representing thedifference between successive levels of the Gaussian pyramid.

In clipped Laplacian blending, one or more intermediate images for themulti-resolution pyramid can be generated by blending the correspondinglevels of the coarse Laplacian pyramid and fine Laplacian pyramid fromthe root level (coarsest level) to the level of the coarse image(described in more detail later with FIG. 6). In other words, theLaplacian pyramid levels at resolutions equal to or coarser than thecoarse image are blended together according to an alpha parameter α. Inaddition, the Laplacian pyramid levels at resolution levels greater thanthe coarse image are taken only from the Laplacian pyramid of the fineimage. The intermediate image can then be constructed by summing theresulting Laplacian pyramid levels. For example, x_((c+1)) is the sum ofthe blended Laplacian pyramid L_((c+1)). This summarized process can berepeated for the other intermediate images, and this process will bedescribed in more detail later.

A block diagram of the process for creating a multi-resolution imagepyramid is illustrated in FIG. 3. A coarse image 310 can be combinedwith the downsampled 322 version of the fine image 312 using structuretransfer 320. The structure transfer operation will be described in moredetail later.

Next, clipped Laplacian blending 330 creates the intermediate levels.Finally, the structure-transferred coarse image 350 (or temporary image)is downsampled 340 so that its new detail structure is propagated toeven coarser levels 360.

The image pyramid construction is performed using preprocessing of theimages. So any 2D or 3D client renderer need not be modified to benefitfrom the improved multi-resolution continuity. The pre-processing cantake place on a server 370 or a computing cloud that has a plurality ofprocessors 380 and memory 390 to service the pre-processing modules oroperations described above. Alternatively, the pre-processing describedmay be embedded in firmware or special purpose hardware.

Image Pyramid Representation

An image pyramid can be denoted by a set x={x₀, . . . , x_(f)} where thecoarsest image x₀ contains a single pixel and each image x_(l) has2^(l)×2^(l) pixels. The most common form is a Gaussian pyramid, in whicheach level contains a low-pass filtered version of a given fine imagex_(f). It is denoted as

, and is formed by successively applying a downsampling filter:

_(f) =x _(f),

_(l−1) =D _(l)

_(l),where the rows of a sparse matrix D_(l) encode the filter weights.

Another useful form is a Laplacian or band pass pyramid, which containsdifferences between successive Gaussian levels. More precisely, eachLaplacian level contains the difference between the current Gaussianlevel and an upsampled version of the next-coarser Gaussian level:L ₀=

₀ ,L _(l)=

_(l) −U _(l−1)

_(l−1).

To define the upsampling matrix U, an interpolatory bicubic filter maybe used, which is also known as Catmull-Rom interpolation. This filteris a tensor product of two 1D filters. Evaluated on the pyramid, each 1Dfilter has weights (−9 111 29 −3)/128 and (−3 29 111 −9)/128 onalternate pixels.

The downsampling filter can be selected by taking the transpose of theupsampling matrix, i.e. D_(l)=U_(l−1) ^(T). Consequently the 1D weightsof the filter are (−3 −9 29 111 111 29 −9 −3)/256. This filter yieldsbetter results than a simple box filter with weights (1 1)/2. While aninterpolatory bicubic filter has been described as an example, there aremany other known filter choices for downsampling and upsampling filters.

The product of the upsampling matrices from coarser level k to finerlevel l can be denoted U_(k) ^(l)=U_(k)U_(k+1) . . . U_(l−1) andsimilarly for the downsampling matrix D_(l) ^(k). The image computationcan be performed in a desired color space (e.g., Lab color space or RGB(Red, Green, and Blue)).

The underlying framework for creating an image pyramid will bedescribed, which will be followed by a more specific description ofexample processes and methods of implementing this technology. Theinputs to the process can be coarse and fine images {circumflex over(x)}_(c) and {circumflex over (x)}_(f), respectively, and the output canbe image pyramid levels {x_(l)}. The goal can be to minimize visualdifferences between successive pyramid levels, while preserving thecolor characteristics of the coarser pyramid levels. These two goals canbe represented as the maximization of an objective:

$\begin{matrix}{{E(x)} = {{\sum\limits_{l = {{1{\ldots f}} - 1}}{{MSSIM}\left( {{D_{1}x_{1}},x_{l - 1}} \right)}} + {\sum\limits_{l = {0{\ldots c}}}{{{Mlc}\left( {{\hat{x}}_{l},x_{l}} \right)}.}}}} & (1)\end{matrix}$

The first term sums the mean structural similarity (MSSIM) of alladjacent pyramid levels. The MSSIM(x, y) of two images x, y is the meanSSIM over all corresponding N×N (e.g., 11×11) pixel neighborhoods u⊂x,v⊂y. The neighborhood SSIM is defined as the product of these factors:SSIM(u,v)=l(u,v)·c(u,v)·s(u,v).

The luminance similarity l, the contrast similarity c, and the structurecomparison s are defined in terms of the mean colors μ, standarddeviations σ, and covariance σ_(uv) of the neighborhoods:

${{l\left( {u,v} \right)} = \frac{{2\mu_{u}\mu_{v}} + c_{1}}{\mu_{u}^{2} + \mu_{v}^{2} + c_{1}}},{{c\left( {u,v} \right)} = \frac{{2\sigma_{u}\sigma_{v}} + c_{2}}{\sigma_{u}^{2} + \sigma_{v}^{2} + c_{2}}},{{s\left( {u,v} \right)} = {\frac{\sigma_{uv} + c_{3}}{{\sigma_{u}\sigma_{v}} + c_{3}}.}}$

These neighborhood statistics are weighted with a spatial Gaussiankernel with a standard deviation of 2 pixels. The small constants c₁,c₂, c₃ exist to ensure numerical stability. The product above simplifiesto:

${{SSIM}\left( {u,v} \right)} = {\frac{\left( {{2\mu_{u}\mu_{y}} + c_{1}} \right)\left( {{2\sigma_{uv}} + c_{2}} \right)}{\left( {\mu_{u}^{2} + \mu_{v}^{2} + c_{1}} \right)\left( {\sigma_{u}^{2} + \sigma_{v}^{2} + c_{2}} \right)}.}$The SSIM can be computed over each color channel independently and themean of the channels can then be taken. The MSSIM measure reaches amaximum value of 1.0 when two images are identical.

The second term of equation (1) measures the color similarity of theoriginal and modified coarse image levels. Specifically, the meanluminance-contrast similarity keeps only the first two factors:

${{{Mlc}\left( {x,y} \right)} = {\frac{1}{x}{\sum_{{u \Subset x},{v \Subset y}}{{l\left( {u,v} \right)} \cdot {c\left( {u,v} \right)}}}}},$and thus ignores structural detail. Because the finer image x_(f) isunaltered in this construction, it may be unnecessary to measure thefiner image's color fidelity.

The process for maximizing E(x) is a nonlinear problem over a largenumber of variables. An approximation scheme follows a three-stepapproach:

Step 1: Replace {circumflex over (x)}_(c) by x_(c) to maximize

$\begin{matrix}{{{\max\limits_{x_{c}}\mspace{11mu}{{Ms}\left( {x_{c},{D_{f}^{c}x_{f}}} \right)}} + {{Mlc}\left( {x_{c},{\hat{x}}_{c}} \right)}},} & (2)\end{matrix}$

where the first term measures only structural compatibility:

${{Ms}\left( {x,y} \right)} = {\frac{1}{x}{\sum_{{u \Subset x},{v \Subset y}}{{s\left( {u,v} \right)}.}}}$

This first step finds a new coarse image that is structurally similar tothe downsampled fine image but whose color characteristics match thoseof the input coarse image {circumflex over (x)}_(c). The structuretransfer process is a fast local algorithm that approximates finding anew coarse image that is structurally similar to the downsampled fineimage and the structure transfer process will be described in furtherdetail later.

Step 2: Create the temporary image levels as

$\begin{matrix}{\min\limits_{x_{c + 1}{\ldots x}_{f - 1}}{\sum\limits_{l = {{c\ldots f} - 1}}{{{MSE}\left( {x_{l},x_{l + 1}} \right)}.}}} & (3)\end{matrix}$

Intuitively, the structural compatibility provided by Step 1 canconstruct the temporary images using the simpler (linear) MSE metric.Furthermore, clipped Laplacian blending provides a fast approximatesolution to this optimization and this will be described in more detaillater.

Step 3: Replace the coarser levels by downsampling x_(c).

This downsampling makes all coarser levels structurally identical (i.e.MSSIM(D_(l)x_(l), x_(l−1))=1 for l≦c). Because Mlc(x_(c), {circumflexover (x)}_(c)) is maximized in Step 1 and downsampling preservesluminance and contrast, Mlc(x_(l), {circumflex over (x)}_(l)) is alsohigh for coarser levels l<c.

Structure Transfer

The coarse and fine images often come from different imaging orphotographic sources, so detail structure in the two images generallydoes not align precisely. Consequently, any linear blending operationeffectively creates a superposition of features from both images.

To address this ghosting problem, the detail from the finer image isused. This choice is motivated by the fact that imagery is typicallycaptured at the limit of the acquisition resolution device, and maytherefore have any number of defects such as chromatic aberration,sensor noise, or demosaicing error. By combining many pixels of thefiner image using a high-quality downsampling, these defects can bereduced.

Therefore, the technology can find a new coarse image x_(c) thatcombines (1) the structural detail of the downsampled fine image D_(f)^(c){circumflex over (x)}_(f) and (2) the local color distribution ofthe original coarse image {circumflex over (x)}_(c). The equationsS=D_(f) ^(c){circumflex over (x)}_(f) and C={circumflex over (x)}_(c)refer to the structure and color images, respectively.

In the following discussion, each color channel of the image will beprocessed separately. For each color channel, a model can be built forthe local distribution of colors in the neighborhood of each pixel inboth images, and a property of the center pixel can be used with respectto the center pixel's neighborhood in the structure image S to selectthe color value with the identical property in the neighborhood in thecolor image C. Two properties that may be used for such calculations maybe the statistical z-score and rank properties, as illustrated in FIG.4. The computation can be performed separately for each color channel.

The Rank process will be discussed first. To transfer rank, thecumulative distribution functions (CDF)

_(S) and

_(C) can be computed for each pixel for values in the image neighborhoodof S and C respectively. For each pixel, the pixel's value v is lookedup in the structure image S and set the output pixel value as v′=

_(T) ⁻¹(

_(S)(v)). This local rank transfer can be viewed as a windowed histogramtransfer operation, which aims to precisely reproduce the color channeldistributions in C. While the Rank process is useful, the process mayintroduce additional noise.

Another method of windowing transfer is the Z-score. Useful results canbe obtained by transferring a z-score for pixel windows (i.e.,approximating the local probability distribution function by aGaussian). Mathematically, the mean μ_(S) and standard deviation σ_(S)of the neighborhood in the structure image are computed. Next, thez-score can be determined: z=(v−μ_(S))/σ_(S) where v is the color of thecenter pixel, and the new color can be obtained as v′=μ_(C)+zσ_(C) whereμ_(C) and σ_(C) are the neighborhood statistics in the color image. Inboth cases, the contributions of pixels in the window can be weightedusing a 2D Gaussian. Useful results can be obtained in one exampleembodiment with a standard deviation of 5 pixels (over a window of 23²pixels).

The z-score transfer approximates the maximization of equation (2),because the z-score transfer preserves the local luminance (mean valueμ) and contrast (σ) of the color image C while altering the detail(z-scores) to correlate with the structure image S. The z-scoretechnique is a greedy approximation in that the technique processes eachpixel independently, while ignoring how the neighboring pixel values aresimultaneously modified. In other embodiments, a more integrated or lessgreedy transfer process can be used.

FIG. 5 illustrates an example process of the method for using thestructure transfer described for generating an image that includes imagestructure detail from a fine image and color from a coarse image. Animage can be obtained that is captured as a coarse image of a definedsubject from a computer memory, as in block 510. Another image can beobtained that has been captured as a fine image of the defined subjectin the coarse image from a computer memory, as in block 520. An exampleof the coarse image is a satellite photo and an example of the fineimage is an aerial photo. The fine image can be downsampled to create atemporary image, as in block 530.

A target pixel in the temporary image can be selected, as in block 540.Next, a target color histogram for a pixel window of the target pixelcan be computed on a per-channel basis, as in block 550. Similarly, thesource color histogram can be determined on a per-channel basis for apixel window of a corresponding pixel in the coarse image using acomputer processor, as in block 560. The structure transfer algorithmcan be performed on a “per-channel” basis for an image that has multiplecolor channels. The image may also be transformed into a different colorspace than the image's original color space to improve the results ofstructure transfer. For example, the input images may be in an RGB (Red,Green, Blue) color space, and then the images may be transformed intothe Lab color space to improve the structure transfer. More generally,structure transfer can be performed in any color space.

A statistic of the target pixel with respect to the target colorhistogram can be computed, as in block 570. For example, a targetpixel's rank can be identified in a cumulative distribution function fora pixel window of the temporary image. Finding the target colorhistogram and the source color histogram for corresponding pixel windowsenables a localized windowed histogram transfer operation to occur for aplurality of target pixels in the temporary image, and allows the targetpixel color to be replaced by the source color from the coarse image.The source color in the source color histogram can be computed with thestatistic, as in block 580. For example, the source color can beselected using the target pixel's rank in the cumulative distributionfunction for the pixel window in the coarse image and that rank can beapplied to the target pixel in the temporary image to select the sourcecolor applied to the target pixel. The target pixel color can then bereplaced by the source color, as in block 590.

Alternatively, the source color to be applied to the target pixel can beidentified by applying a color from the correlated pixel in a coarseimage that has the same standard deviation in the pixel window as thetarget pixel in the temporary image. A color probability distributionfunction can be used such as a Gaussian probability distributionfunction. Accordingly, a z-score can be computed for a target pixel'scolor in a color probability distribution function for a local pixelwindow. Then the z-score can be applied to the color probabilitydistribution function for the source's local pixel window of acorresponding pixel in the coarse image in order to select the sourcecolor from the coarse image that is applied to the target pixel.

Pyramid Construction

As discussed previously, to create the temporary images {x_(l)|c<l<f},the pixel differences between successive levels are minimized:

$\begin{matrix}{{\min\limits_{x_{c + 1}{\ldots x}_{f - 1}}{\sum\limits_{l = {{c\ldots f} - 1}}{{MSE}\left( {x_{l},x_{l + 1}} \right)}}},} & (4)\end{matrix}$

The precise definition of the mean squared error term MSE(x_(l),x_(l+1)) is relevant. Two definitions can be considered. The firstapproach corresponds to a simple form of linear interpolation and leadsto undesirable blurring. The second approach, which is defined here asclipped Laplacian blending is better able to preserve image detail.

Since equation (4) defines a sparse linear system, the linear system canbe solved using an iterative solver. However, by applying certainconstraints on the downsampling filter D and upsampling filter U, theglobal minimum of equation (4) can be directly obtained using moreefficient algorithms. A specific constraint is that the filters areassumed to be orthogonal and transposes of each other:D _(l) D _(l) ^(T)=¼I and D _(l) =U _(l−1) ^(T).

One low-pass filter that satisfies both constraints is the box filter,and the box filter is undesirable for image resampling due to its lessdesirable frequency characteristics. Fortunately, a fast constructionapproach as defined here incurs a very small approximation error inconjunction with higher-order filters which have better frequencyresponse but are not strictly orthogonal and therefore do not satisfythe assumption. The assumption and/or constraint described here is usedto make the analysis easier. In practice, this assumption (orconstraint) does not hold true, but the error introduced due to thisincorrect assumption can be shown to be small.

Simple Linear Interpolation

The inter-level MSE between the finer image and the upsampled coarserimage can first be defined as:MSE(x _(l) ,x _(l+1))=4^(−l) ∥x _(l+1) −U _(l) x _(l)∥².  (5)

Here the factor 4^(−l) accounts for the number of pixels at level l whencomputing the mean error. Intuitively, minimizing equation (5) seeks tomake every pixel of the finer image look like a magnified version of thecoarser image.

To find the images {x_(l)} minimizing equations (4) using (5), thepartial derivative is taken with respect to a level x_(l) and set tozero:2(4^(−(l−1)))(x _(l) −U _(l−1) x _(l−1))−2(4^(−l))U _(l) ^(T)(x _(l+1)−U _(l) x _(l))=0(¼U _(l) ^(T) U _(l) +I)x _(l) =U _(l−1) x _(l−1)+¼U _(l) ^(T) x _(l+1).The definition that U_(l−1)=4D_(l) ^(T) and D_(l)U_(l−1)=I lets U_(l)^(T)U_(l) be rewritten as 4D_(l+1)U_(l)=4I to obtain the localconstraints:x _(l)=½(U _(l−1) x _(l−1) +D _(l+1) x _(l+1)).  (6)In other words, the image at a given level should equal the average ofits adjacent levels (appropriately resampled).

A direct solution to this variational problem is found by a simplelinear resampling and interpolation of the original coarse and fineimages:

$\begin{matrix}{x_{l} = {{{\left( {1 - \alpha_{l}} \right)U_{c}^{l}x_{c}} + {\alpha_{l}D_{f}^{l}x_{f}\mspace{14mu}{with}\mspace{14mu}\alpha_{l}}} = {\frac{l - c}{f - c}.}}} & (7)\end{matrix}$

However, this solution is less desirable because the detail of the fineimage is attenuated by the blurry upsampling of the coarse image.

Clipped Laplacian Blending

In the Clipped Laplacian approach, the inter-level visual difference canbe defined as the MSE between the downsampled finer image and thecoarser image:MSE(x _(l) ,x _(l+1))=4^(−l) ∥D _(l+1) x _(l+1) −x _(l)∥².  (8)

This small change to the objective function fundamentally alters theresult. Specifically, the downsampling constraint is less demanding.Whereas the earlier function in equation (5) sought to make all n²pixels of the finer image look like the magnified coarser image, theimproved function (8) seeks to make (n/2)² weighted averages of thefiner image look like the coarser image.

To find the {x_(l)} minimizing equations (4) using (8), the partialderivative is taken with respect to a level x_(l) and set to zero:2(4^(−(l−1)))D _(l) ^(T)(D _(l) x _(l) −x _(l−1))−2(4^(−l))(D _(l+1) x_(l+1) −x _(l))=0.

Pre-multiplying both sides by ½4^(l)D_(l), the result is obtained:4D _(l) D _(l) ^(T)(D _(l) x _(l) −x _(l−1))−D _(l)(D _(l+1) x _(l+1) −x_(l))=0.

Using the identity D_(l)D_(l) ^(T)=¼I, this is obtained:(D _(l) x _(l) −x _(l−1))−(D _(l+1) ^(l−1) x _(l+1) −D _(l) x _(l))=0(D _(l) +D _(l))x _(l) =x _(l−1) +D _(l+1) ^(l−1) x _(l+1).

Thus, the local constraint is found:D _(l) x _(l)=½(x _(l−1) +D _(l+1) ^(l−1) x _(l+1)).  (9)

In other words, the downsampling of each image should be a blendedcombination of the next-coarser image and the twice-downsamplednext-finer image.

There is an efficient construction that satisfies the local constraints(9), and therefore globally minimizes equation (8). This can be calledthe Laplacian Pyramid method which will be presented now in threesuccessively more efficient computational forms.

Solution Form 1. The Gaussian pyramid

^(x) ^(f) and Laplacian pyramid L^(x) ^(f) of image x_(f), are firstformed as defined previously, and L^(x) ^(c) is similarly constructedfrom the coarse image. To form each intermediate image x_(l); a newLaplacian pyramid L^(x) ^(l) is created by blending the correspondingLaplacian levels of the two images from the root level (coarsest level)to the level of the coarse image:

$\begin{matrix}{\mathcal{L}_{k}^{x_{l}} = \left\{ \begin{matrix}{{\left( {1 - \alpha_{l}} \right)\mathcal{L}_{k}^{x_{c}}} + {\alpha_{l}\mathcal{L}_{k}^{x_{f}}}} & {k \leq c} \\\mathcal{L}_{k}^{x_{f}} & {{k > c},}\end{matrix} \right.} & (10)\end{matrix}$where α_(l) is defined as in equation (7). The process can be calledclipped Laplacian blending as illustrated in FIG. 6. Clipped Laplacianblending creates intermediate-resolution images by smoothlytransitioning the coarse levels of the Laplacian pyramids whileiteratively adding intact fine detail. If the two Laplacian pyramidswere blended across all levels, this would recreate the less effectivesolution described that uses simple linear interpolation.

Each temporary image can be reconstructed as:

$\begin{matrix}\begin{matrix}{x_{l} = {\sum\limits_{k = {0{\ldots l}}}{U_{k}^{l}\mathcal{L}_{k}^{x_{l}}}}} \\{= {{U_{l - 1}\left( {{\ldots\left( {{U_{0}\left( \mathcal{L}_{0}^{x_{l}} \right)} + \mathcal{L}_{1}^{x_{l}}} \right)} + \ldots} \right)} + {\mathcal{L}_{l}^{x_{l}}.}}}\end{matrix} & \begin{matrix}(11) \\\; \\(12)\end{matrix}\end{matrix}$

Solution form 2. The same solution can also be obtained by linearlyblending the coarse image x_(c) with the coarse version

_(c) ^(x) ^(f) of the fine image, and adding back the Laplacian detailL_(c+1) ^(x) ^(f) . . . L_(l) ^(x) ^(f) of the fine image:

$\begin{matrix}{x_{l} = {{U_{c}^{l}\left( {{\left( {1 - \alpha_{l}} \right)x_{c}} + {\alpha_{l}{??}_{c}^{x_{f}}}} \right)} + {\sum\limits_{k = {c + {1{\ldots l}}}}{U_{k}^{l}{\mathcal{L}_{k}^{x_{f}}.}}}}} & (13)\end{matrix}$

Solution form 3. Finally, the expression can be transformed once againto obtain an even simpler form that avoids having to compute and storeLaplacian pyramids altogether. From equation (13) we obtain

$\begin{matrix}{{x_{l} = {{{U_{c}^{1}\left( {1 - \alpha_{l}} \right)}\left( {x_{c} - {??}_{c}^{x_{f}}} \right)} + {U_{c}^{l}{??}_{c}^{x_{f}}} + {\sum\limits_{k = {c + {1{\ldots l}}}}{U_{k}^{l}\mathcal{L}_{k}^{x_{f}}}}}}{{x_{l} = {{\left( {1 - \alpha_{l}} \right)U_{c}^{1}d_{c}} + {??}_{l}^{x_{f}}}},{{{with}\mspace{14mu} d_{c}} = {x_{c} - {??}_{c}^{x_{f}}}}}} & (14)\end{matrix}$

In this form as illustrated in FIG. 7, the difference d_(c) between thecoarse image and the downsampled fine image is computed, that differenceis upsampled to the intermediate level, and the upsampled difference isfaded into the Gaussian pyramid. FIG. 7 illustrates the process as anefficient blending algorithm with 3 steps: (1) downsampling to formGaussian pyramid 710, (2) coarse-level differencing 720, and (3) fadingthe difference into the pyramid 730.

The solution of equation (14) offers a simple recurrence that lets alllevels be evaluated in an efficient sequence of two passes over apyramid structure. The results of this process are much sharper than theprevious method of simple linear interpolation. A pseudo-code listing ofthe method is as follows:

(x_(c+1) ... x_(f−1)) ←ClippedLaplacianBlend(x_(c), x_(f)) {  G_(f) =x_(f) // Create the Gaussian pyramid of x_(f)  for l = f − 1 ... c // bysuccessive fine-to-coarse   G_(l) = D_(l+1)G_(l+1) // downsamplingoperations.  d = x_(c) − G_(c) // Compute the coarse difference.  for l= c + 1 ... f − 1 // Traverse the Gaussian pyramid,   d = U_(l−1)d// upsampling the difference image,   α_(l) = (l − c)/(f − c) // andadding a faded fraction   x_(l) = G_(l) + (1 − α_(l))d // of it at eachlevel. }

FIG. 8 is a flowchart illustrating efficient operations for generating amulti-resolution image pyramid used in visual transitions acrossmultiple viewing scales. A coarse image and a fine image of a definedsubject can be obtained from a computer memory, as in block 810 and 820.A Gaussian image pyramid with a plurality of downsampled images can begenerated using the fine image, as block 830.

A temporary image can be defined as a level within the Gaussian imagepyramid that has a same resolution as the coarse image, and anintermediate image can be defined that is a copy of the temporary image,as in block 840. A structure transfer operation can then be applied tothe intermediate image to transfer color detail from the coarse image tothe intermediate image, as in block 850. The use of the structuretransfer operation is an optional part of the process as shown by thedotted line in FIG. 8, and the clipped Laplacian blending method can beused independent from the structure transfer method.

In addition, a difference image can be generated or computed from adifference between the intermediate image with structure transferreddetails and the temporary image, as in block 860. A difference image canthen be upsampled into successively finer levels of the Gaussian imagepyramid. The difference image can be upsampled for each pyramid leveland the upsampled difference image can be blended into each image ateach level of the Gaussian image pyramid.

In addition, the difference image can be blended into the Gaussian imagepyramid with alpha blending (i.e., linear interpolation), as in block870. The alpha blending can be a graded amount of alpha blending, andthe graded alpha blending can increase as the size of the downsampledimages in the Gaussian image pyramid decreases. The graded amount ofalpha blending at each level can be defined by

${1 - \frac{\left( {l - c} \right)}{\left( {f - c} \right)}};$where l is the index value of a level of the Gaussian image pyramidbeing blended, f is the level index value of the fine image and c is thelevel index value of the coarse image.

FIG. 9 illustrates a system for generating a multi-resolution imagepyramid used in visual transitions. Each of the modules described belowmay be a hardware module that performs the specified processes.Alternatively, each of the modules may be a server with a plurality ofprocessors that are networked together to perform the desired processesfor the module. An example of this may be a blade server or computingfarm.

An acquisition module 910 can be configured to obtain a coarse image ofa defined subject. The coarse image may have a specified resolutionsize. The acquisition module can also obtain a fine image of the definedsubject that corresponds to a view of the defined subject. As discussedbefore, these images may be satellite and aerial images or the imagescan be different levels of resolution for textures.

A downsampling module 920 can downsample the fine image to create atemporary image having the size of the coarse image. Once thedownsampling has been performed, a structure transfer module 930 canapply a structure transfer operation to the temporary image to transfercolor from the coarse image to the temporary image to form anintermediate image. The structure transfer can retain the structuraldetail from the temporary image.

An image difference module 940 can compute a difference image from adifference between the intermediate image with structure transferreddetails and the temporary image. An upsampling and blending module 950can upsample the difference image into successively finer levels of theGaussian image pyramid using blending of the difference image into theGaussian image pyramid with a graded level of alpha blending for animage level.

While this technology has been described using orthogonal filters, theprocesses can also be used with non-orthogonal filters. The fastalgorithms developed in the preceding sections assume the use oforthogonal up/downsampling filters. However, the cubic filters we havechosen are not strictly orthogonal and will therefore introduce somesmall amount of error. An error analysis for the use of non-orthogonalfilters in the described technology will now be discussed. The resultsfrom the present technology can be compared against reference solutionsobtained by directly minimizing equation (4) using the Gauss-Seideliteration. Measuring the error term in equation (4) for both sets ofresults, the clipped Laplacian blending results typically differ by lessthan 1% from reference images, with the greatest difference being under3%. Subjectively, the results are visually indistinguishable.

An example application of the present technology is geographic mapping.Because the imagery can be quite large (e.g. potentially covering theEarth), the images are typically partitioned into tiles, both forefficient processing and for fast delivery over the Internet.Fortunately, the techniques discussed (structure transfer and clippedLaplacian blending) may operate with access to just local data.

The images

_(l), x_(l), d_(l) may be maintained in a few thousand tiles incorrespondence with the input. Minimization of costly disk accesses isalso valuable. However, in the course of processing a large imagepyramid some tiles are temporarily stored to disk while new tiles arecomputed. To effectively manage this problem, a tile cache can betailored to the access pattern of the described processes.

The tile access order can be known ahead of time, so an optimizedcaching strategy can be employed. This strategy is to evict the tilethat will be needed furthest in the future. Furthermore, the tile accessorder can be used to pre-cache tiles in a background thread. For anygiven tile, the tile data dependency order is typically known. Thus,after a tile has been computed, the tile's dependencies may be examinedand those tiles which are not needed to compute future tiles can beimmediately evicted. Generating the finest-level tiles in Hilbert-curveorder also provides effective caching performance.

An example dataset can be imagery of the Earth's surface sampled over aregular grid under a Mercator projection. In the image pyramid, thecoarsest resolution (level 0) contains a single 256² image tile. Thefinest level (level 20) conceptually contains 2⁴⁰ such tiles, but isdefined quite sparsely. The example input imagery may be obtained fromseveral sources including: level 8 (4-Gpixel) may be satellite imagery,level 13 (4-Tpixel) may be “Landsat” satellite imagery, and levels 14and above may contain sparsely defined aerial photography. Therefore, inmost areas there can be two discontinuous transitions across scales:from level 8 to 9, and from level 13 to 14.

The described technology can improve both of these transitions. In thisexample, corrections can be made over the whole earth for level 8 to 9,and over several regions for level 13 to 14. To correct the appearancediscontinuity from level 8 to 9, level 8 can be used as the coarse image{circumflex over (x)}_(c) and level 11 as the fine image {circumflexover (x)}_(f), and modified levels were 8 through 10. Level 8 can bereplaced by the structure-transferred result x_(c). To correct thediscontinuity from level 13 to 14, levels 13 and 17 can be used as{circumflex over (x)}_(c) and {circumflex over (x)}_(f) respectively. Inthis example case, increasing the number of transition levels from 3 to4 may be beneficial because of the greater disparity in appearancebetween these image sources. Modifying the detail structure does notresult in objectionable spatial seams in the case where the fine-scalecontent is sparsely defined.

Technology has been described that can enable fast creation of smoothvisual pyramids from dissimilar imagery, and practical results have beendemonstrated on large datasets with a variety of content. The visuallycontinuous image pyramid can combine different image data sources atdifferent scales.

Some of the functional units described in this specification have beenlabeled as modules, in order to more particularly emphasize theirimplementation independence. For example, a module may be implemented asa hardware circuit comprising custom VLSI circuits or gate arrays,off-the-shelf semiconductors such as logic chips, transistors, or otherdiscrete components. A module may also be implemented in programmablehardware devices such as field programmable gate arrays, programmablearray logic, programmable logic devices or the like.

Modules may also be implemented in software for execution by varioustypes of processors. An identified module of executable code may, forinstance, comprise one or more blocks of computer instructions, whichmay be organized as an object, procedure, or function. Nevertheless, theexecutables of an identified module need not be physically locatedtogether, but may comprise disparate instructions stored in differentlocations which comprise the module and achieve the stated purpose forthe module when joined logically together.

Indeed, a module of executable code may be a single instruction, or manyinstructions, and may even be distributed over several different codesegments, among different programs, and across several memory devices.Similarly, operational data may be identified and illustrated hereinwithin modules, and may be embodied in any suitable form and organizedwithin any suitable type of data structure. The operational data may becollected as a single data set, or may be distributed over differentlocations including over different storage devices. The modules may bepassive or active, including agents operable to perform desiredfunctions.

Furthermore, the described features, structures, or characteristics maybe combined in any suitable manner in one or more embodiments. In thepreceding description, numerous specific details were provided, such asexamples of various configurations to provide a thorough understandingof embodiments of the described technology. One skilled in the relevantart will recognize, however, that the technology can be practicedwithout one or more of the specific details, or with other methods,components, devices, etc. In other instances, well-known structures oroperations are not shown or described in detail to avoid obscuringaspects of the technology.

Although the subject matter has been described in language specific tostructural features and/or operations, it is to be understood that thesubject matter defined in the appended claims is not necessarily limitedto the specific features and operations described above. Rather, thespecific features and acts described above are disclosed as exampleforms of implementing the claims. Numerous modifications and alternativearrangements can be devised without departing from the spirit and scopeof the described technology.

1. A method performed by one or more computers comprising storage andone or more processors, the method for generating a multi-resolutionimage pyramid, comprising: obtaining and storing in the storage an imagecaptured as a coarse image of a defined subject; obtaining and storingin the storage another image captured as a fine image of the definedsubject; downsampling, by the one or more processors, the fine image tocreate a temporary image that is stored in the storage; applying, by theprocessor, a structure transfer operation to the temporary image totransfer color detail from the coarse image, while retaining structuraldetail from the temporary image; and applying, by the one or moreprocessors, a blending operation between the temporary image and thefine image to construct an intermediate image for at least oneintermediate level in the multi-resolution image pyramid between thefine image and the coarse image, and storing the intermediate image inthe storage.
 2. The method as in claim 1, further comprising applying ablending operation that is clipped Laplacian blending.
 3. The method asin claim 1, further comprising applying a blending operation that blendsa Laplacian pyramid from the fine image with a Laplacian image generatedfrom the temporary image.
 4. The method as in claim 1, furthercomprising: forming a fine Laplacian image pyramid having a plurality ofdownsampled images from the fine image; constructing a coarse Laplacianimage pyramid having a plurality of downsampled images from the coarseimage; generating each intermediate image by forming a third Laplacianpyramid by blending the corresponding levels of the coarse Laplacianpyramid and fine Laplacian pyramid from a root level to the level of thecoarse image.
 5. The method as in claim 1, further comprising retrievingthe coarse image and fine image of the defined subject from a computerreadable storage medium.
 6. The method as in claim 2, wherein theoperation of applying a structure transfer operation and applying ablending operation to the temporary image are performed by a server by acomputer processor.
 7. A method for generating a multi-resolution imagepyramid used in visual transitions across multiple viewing scales,comprising: obtaining a coarse image of a defined subject from acomputer memory, the coarse image having a size; obtaining a fine imageof the defined subject from a computer memory that corresponds to a viewof the defined subject at a finer resolution than the coarse image;generating a Gaussian image pyramid having a plurality of downsampledimages using the fine image; defining a temporary image as a levelwithin the Gaussian image pyramid that has a same resolution as thecoarse image and an intermediate image that is a copy of the temporaryimage; computing a difference image from a difference between theintermediate image and the temporary image using a processor; upsamplinga difference image into successive finer levels of the Gaussian imagepyramid and blending the difference image into the Gaussian imagepyramid with alpha blending.
 8. A method as in claim 7, furthercomprising; applying a structure transfer operation to the intermediateimage to transfer color detail from the coarse image to the intermediateimage using a processor; and computing a difference image from adifference between the intermediate image with structure transferreddetails and the temporary image using a processor.
 9. A method as inclaim 7, wherein the step of upsampling the difference image furtherincludes blending the difference image into each image at each level ofthe Gaussian image pyramid.
 10. A method as in claim 9, furthercomprising adding the upsampled difference image back into each level ofGaussian image pyramid using a graded amount of alpha blending.
 11. Amethod as in claim 10, further comprising adding the upsampleddifference image back into a selected level of the Gaussian imagepyramid using a graded amount of alpha blending that increases as thesize of the downsampled images in the Gaussian image pyramid decreases.12. A method as in claim 7, further comprising adding the upsampleddifference image back into each level of Gaussian image pyramid using agraded amount of alpha blending at each level defined by${1 - \frac{\left( {l - c} \right)}{\left( {f - c} \right)}};$ where lis the index value of a level of the Gaussian image pyramid beingblended, f is the level index value of the fine image and c is the levelindex value of the coarse image.
 13. A method as in claim 7, wherein thecoarse image is a satellite photo of a defined geographic area and thefine image is an aerial photo of the defined geographic area.
 14. Asystem for generating a multi-resolution image pyramid used in visualtransitions, comprising: an acquisition module configured to obtain acoarse image of a defined subject, the coarse image having a size, and afine image of the defined subject that corresponds to a view of thedefined subject; a downsampling module configured to downsample the fineimage to create a temporary image having the size of the coarse image; astructure transfer module configured to apply a structure transferoperation to the temporary image to transfer color from the coarse imageto the temporary image, while retaining structural detail from thetemporary image to form an intermediate image; an image differencemodule configured to compute a difference image from a differencebetween the intermediate image with structure transferred details andthe temporary image; and an upsampling and blending module configured toupsample the difference image into successively finer levels of theGaussian image pyramid using blending of the difference image into theGaussian image pyramid with a graded level of alpha blending for animage level.
 15. The system as in claim 14, wherein the structuretransfer module further is configured to compute a difference image froma difference between the intermediate image with structure transferreddetails and the temporary image using a processor.
 16. The system as inclaim 14, wherein the upsampling and blending module is configured toblend the difference image into each image at each level of the Gaussianimage pyramid.
 17. The system as in claim 16, wherein the upsampling andblending module is configured to add the upsampled difference image backinto each level of Gaussian image pyramid using a graded amount of alphablending.
 18. The system as in claim 17, wherein the upsampling andblending module is configured to add the upsampled difference image backinto a selected level of the Gaussian image pyramid using a gradedamount of alpha blending that increases as the size of the downsampledimages in the Gaussian image pyramid decreases.
 19. The system as inclaim 14, wherein the upsampling and blending module is configured toadd the upsampled difference image back into each level of Gaussianimage pyramid using a graded amount of alpha blending at each leveldefined by${1 - \frac{\left( {l - c} \right)}{\left( {f - c} \right)}};$ where lis the index value of a level of the Gaussian image pyramid beingblended, f is the level index value of the fine image and c is the levelindex value of the coarse image.
 20. The system as in claim 14, whereinthe coarse image is a satellite photo of a defined geographic area andthe fine image is an aerial photo of the defined geographic area.